When EQing an amp, what's an appropriate way of doing it? Should I stand right in front of it while peering in front of it? Should I get down to the speaker level? Should I go back a few feet and EQ it? Should I go back however man feet and get down to speaker level?

I have this really fat and warm tone that I love right now, but I'm standing a few feet away from it, not at speaker level. When I step back further and further the sound just gets harsh and brittle. What do I do to achieve the same tone that I hear when I EQ it as I've been doing?
Not sure what to say about this, if you're playing live, the sound each member of your audience is hearing can vary the same way it varies for you when you're standing in different places. If you know that you'll be mic'ing the amp (for recording, or p.a.), then I'd say the sound you're getting close to the speaker is what would be important.
Of course volume plays a role too, you'll probably find that the EQ you use at low volume will change a fair bit once you crank it up.

Sorry if this isn't much help!
i would just eq it to where you actually play or to where your audience will be.
most likely the change in tone dynamics is based on the room shape/obstruction. like if you play some music on a stereo and then go into another room and close the door its just sounds like bass.
a rule of thumb when EQing is doing highs>mid>bass

this probably doesnt help much but maybe you can implement it to help a bit
turn it up i dont know that's a good question man I'm experienced and that threw for a loop. all i can say is good luck and i hope somebody else can help.
Yeah I think the volume might definitely be a problem.

Thanks souldriver. I'll try re-EQing my amp that way.

I'm no expert in the studies of sound travel or what have you, but do high frequencies and mid frequencies travel farther? Could that be the reason for this?

Another possible reason is one that I just thought of. I'm using a 4x10 and a 4x12. The 4x10 is open back. From what I know about open backs, they tend to be louder. The sound goes out the back and reverberates around the room. Both the cabs are against a plastic or metal plate for photo machine. That might be why it sounds harsh and brittle. The 4x10s aren't necessarily the warmest things in the world either.

These are definitely possibilities, but maybe not. Thanks for the help so far but I still want to hear if I'm just doing something wrong or if I can fix it.